Overview
This workshop reviews how to count and apply significant figures (sig figs) in measurements and calculations, including addition, subtraction, multiplication, and division.
Importance of Significant Figures
- Significant figures reflect the certainty of a measurement based on the instrument used.
- Preserving significant figures in calculations ensures measurement certainty is maintained.
Rules for Counting Significant Figures
- All non-zero digits are always significant.
- Zeros between non-zero digits are significant (e.g., 28.03 has four sig figs).
- Zeros to the left of the first non-zero digit are not significant (e.g., 0.0032 has two sig figs).
- Zeros at the end of a number:
- After a decimal point: always significant (e.g., 45.000 has five sig figs).
- Before a decimal point and after a non-zero digit: significant (e.g., 140.00 has five sig figs).
- Before an implied decimal point: ambiguous—use scientific notation to clarify (e.g., 1200 = 1.2 × 10³, two sig figs).
Special Cases
- Temperature measurements (in any unit) have as many sig figs as digits shown (e.g., 300 K has three sig figs).
Examples of Counting Significant Figures
- 554: three sig figs.
- 101: three sig figs (interior zero is significant).
- 0.0099: two sig figs (leading zeros not significant).
- 145.00: five sig figs (trailing zeros after decimal are significant).
- 21000 (no decimal): ambiguous; scientific notation required.
Rules for Calculations with Significant Figures
Multiplication and Division
- The result has as many sig figs as the factor with the fewest sig figs.
- Example: 1.052 × 12.054 × 0.53 = 6.7 (two sig figs).
Addition and Subtraction
- The result has the same number of decimal places as the value with the fewest decimal places.
- Example: 2.345 + 0.07 + 2.9975 = 5.41 (two decimal places).
Worked Examples
- Multiplication/Division: 3.1107 × 9441 × 0.0301 ÷ 2.31 = 0.381 (rounded to 3 sig figs).
- Addition/Subtraction: 0.881 + 132.1 - 12.02 = 121.0 (one decimal place).
- Mixed operations: Complete addition/subtraction first (use decimal place rule), then apply sig fig rule for multiplication/division.
Key Terms & Definitions
- Significant Figures (Sig Figs) — the digits in a measurement that indicate known precision.
- Leading Zeros — zeros before the first non-zero digit; not significant.
- Interior Zeros — zeros between non-zero digits; always significant.
- Trailing Zeros — zeros at the end of a number; significant if after a decimal or clarified with scientific notation.
- Ambiguous Zeros — zeros that may or may not be significant without more context; use scientific notation to clarify.
Action Items / Next Steps
- Complete extra exercises from chapters 1–4 on Moodle to practice significant figures.
- Review textbook sections on logarithms and anti-logarithms if interested.
- Remember to apply these sig fig rules on midterms and final exams.